H M command R G N W D Q Mathematics 30-1 Quiz 1.3 - TS 3. The exact roots of the rational equation -+ - 4 - = 1 are x x+ 3 A. 2+ V13 x = atV 13 B. -2+ 13 = 2 - C. 2+ / 13 13 2 -2+ 13 2 Hint: The request for exact roots indicates decimal values are not acceptable. Multiply each term by a common denominator. Use the quadratic formula, not technology, to determine the roots. 4. Which of the following characteristics correspond(s) to the graph of the function G(x) = 2x + 3x -2? x+2 A. Vertical asymptote and point of discontinuity B. Point of discontinuity C. Horizontal asymptote D. Vertical asymptote Hint: Factor to determine the behaviour of the graph of the function at the non-permissible values. bdine Numerical Response 2. The positive root, to the nearest hundredth, of the rational equation x - 1 =- 6 x - 3 Hint: Technology may be used. 2 + 1 7 = 4.65 4.7 5. Consider the function f(x) = 4x 9 - x2 . Which of the following statements is false? A . The graph of f(x ) has 2 vertical asymptotes. The function f(x ) is not defined when x = 0. The function f(x) is a rational function. The function f(x ) has one zero. Hint: Factor the difference of squares in the denominator.control option amma Mathematics 30-1 Quiz 1.3 - TS Value 9 PART A: MULTIPLE CHOICE/NUMERICAL RESPONSE This quiz includes multiple choice and numerical response questions. For multiple choice questions, select the best answer. For numerical response questions, enter the numerical values into the space provided. 1. Which of the following strategies cannot be used to solve the rational equation x + 2 - =x+3. 3x + 2 x - 1 A. Graph the left side as Y, and the right side as Y2, and then determine the point(s) of intersection of the two graphs. B. Graph the left side as Y, and the right side as Y2, and then determine the x-intercept(s) of the two graphs. C. Rearrange the equation so it equals zero, graph the non-zero side of the equation as Y1, and then determine the x-intercept(s). D. Rearrange the equation so it equals zero, graph the left side as Y, graph Yz = 0, and then determine the point(s) of intersection of the two graphs. Hint: Consider the graphing calculator references in the alternatives. Graphs labelled Y, and Y2 are used with Texas Instruments graphing calculators, such as the TI-83 or TI-84. For other graphing calculators, think of Y, and Yz as the first and second graphs. 5 2. When solving the equation x - 1 x + 1 -+ -2=-6 algebraically, the equation can be rearranged to which equivalent quadratic equation, where x * - 1, 1? + =6 60 2 + 7x - 3: 0 A. 6x2 + 7x - 3= 0 - 1 B. 6x2 + 7x - 1 = 0 6x2 + 7x + 3= 0 " . s( x +1 ) + 2 ( x -1) . -6 (xt ) ( x- 1 ) D. 6x2 + 7x + 13 = 0 6 * 2 - 6 + 7* + 3 : 0 6 *2 + 7 x- 320 Hint: Multiply each term by a common denominator. Numerical Response 1 . Given the function f(x) = 2x-x - 1 2x2 - 2x , what is the sum of the coefficients and constants remaining in the function after it has been simplified? Hint: Factor fully to simplify. Review the definitions for coefficients and constants. Alberta Distance Learning CentreMathematics 30-1 Quiz 1.3 - TS 6. The graph of which of the following functions has a point of discontinuity at x = 2 and a vertical asymptote at x = 1? A. f(x ) = 3x - 4x+ 1 3x2 - x B. f(x ) = 3x + 4x+ 1 3x- 1 C. f(x ) = 3x - 1 3x2 + 4x + 1 D. f(x ) = 3x2 - x 3x2 - 4x + 1 Hint: Factor fully. The factor that is eliminated corresponds to the point of discontinuity. Numerical Response 3. 2 The largest non-permissible value of x for the rational equation x2 - 5x + 6 x2-25 x = 1 is Hint: Factor each denominator fully to determine the non-permissible values of x. END OF QUIZ Total Marks: 9 W Alberta Distance Learning Centre